(-2x-2y)(3x+6y)=0

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Solution for (-2x-2y)(3x+6y)=0 equation: 


Simplifying
(-2x + -2y)(3x + 6y) = 0

Multiply (-2x + -2y) * (3x + 6y)
(-2x * (3x + 6y) + -2y * (3x + 6y)) = 0
((3x * -2x + 6y * -2x) + -2y * (3x + 6y)) = 0

Reorder the terms:
((-12xy + -6x2) + -2y * (3x + 6y)) = 0
((-12xy + -6x2) + -2y * (3x + 6y)) = 0
(-12xy + -6x2 + (3x * -2y + 6y * -2y)) = 0
(-12xy + -6x2 + (-6xy + -12y2)) = 0

Reorder the terms:
(-12xy + -6xy + -6x2 + -12y2) = 0

Combine like terms: -12xy + -6xy = -18xy
(-18xy + -6x2 + -12y2) = 0

Solving
-18xy + -6x2 + -12y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-6'.
-6(3xy + x2 + 2y2) = 0

Factor a trinomial.
-6((x + y)(x + 2y)) = 0

Ignore the factor -6.

Subproblem 1
Set the factor '(x + y)' equal to zero and attempt to solve:

Simplifying
x + y = 0

Solving
x + y = 0

Move all terms containing x to the left, all other terms to the right.

Add '-1y' to each side of the equation.
x + y + -1y = 0 + -1y

Combine like terms: y + -1y = 0
x + 0 = 0 + -1y
x = 0 + -1y
Remove the zero:
x = -1y

Simplifying
x = -1y

Subproblem 2
Set the factor '(x + 2y)' equal to zero and attempt to solve:

Simplifying
x + 2y = 0

Solving
x + 2y = 0

Move all terms containing x to the left, all other terms to the right.

Add '-2y' to each side of the equation.
x + 2y + -2y = 0 + -2y

Combine like terms: 2y + -2y = 0
x + 0 = 0 + -2y
x = 0 + -2y
Remove the zero:
x = -2y

Simplifying
x = -2y
Solution
x = {-1y, -2y}

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